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Algebraic Prerequisites1.1 Graphing Basics1.1.1 Using the Cartesian System1.1.2 Thinking Visually1.2 Relationships between Two Points1.2.1 Finding the Distance between Two Points1.2.2 Finding the Second Endpoint of a Segment1.3 Relationships among Three Points1.3.1 Collinearity and Distance1.3.2 Triangles1.4 Circles1.4.1 Finding the Center-Radius Form of the Equation of a Circle1.4.2 Finding the Center and Radius of a Circle1.4.3 Decoding the Circle Formula1.4.4 Solving Word Problems Involving Circles1.5 Graphing Equations1.5.1 Graphing Equations by Locating Points1.5.2 Finding the x- and y-Intercepts of an Equation1.6 Function Basics1.6.1 Functions and the Vertical Line Test1.6.2 Identifying Functions1.6.3 Function Notation and Finding Function Values1.7 Working with Functions1.7.1 Determining Intervals Over Which a Function Is Increasing1.7.2 Evaluating Piecewise-Defined Functions for Given Values1.7.3 Solving Word Problems Involving Functions1.8 Function Domain and Range1.8.1 Finding the Domain and Range of a Function1.8.2 Domain and Range: One Explicit Example1.8.3 Satisfying the Domain of a Function1.9 Linear Functions: Slope1.9.1 An Introduction to Slope1.9.2 Finding the Slope of a Line Given Two Points1.9.3 Interpreting Slope from a Graph1.9.4 Graphing a Line Using Point and Slope1.10 Equations of a Line1.10.1 Writing an Equation in Slope-Intercept Form1.10.2 Writing an Equation Given Two Points1.10.3 Writing an Equation in Point-Slope Form1.10.4 Matching a Slope-Intercept Equation with Its Graph1.10.5 Slope for Parallel and Perpendicular Lines1.11 Graphing Functions1.11.1 Graphing Some Important Functions1.11.2 Graphing Piecewise-Defined Functions1.11.3 Matching Equations with Their Graphs1.12 Manipulating Graphs: Shifts and Stretches1.12.1 Shifting Curves along Axes1.12.2 Shifting or Translating Curves along Axes1.12.3 Stretching a Graph1.12.4 Graphing Quadratics Using Patterns1.13 Manipulating Graphs: Symmetry and Reflections1.13.1 Determining Symmetry1.13.2 Reflections1.13.3 Reflecting Specific Functions1.14 Quadratic Functions: Basics1.14.1 Deconstructing the Graph of a Quadratic Function1.14.2 Nice-Looking Parabolas1.14.3 Using Discriminants to Graph Parabolas1.14.4 Maximum Height in the Real World1.15 Quadratic Functions: The Vertex1.15.1 Finding the Vertex by Completing the Square1.15.2 Using the Vertex to Write the Quadratic Equation1.15.3 Finding the Maximum or Minimum of a Quadratic1.15.4 Graphing Parabolas1.16 Composite Functions1.16.1 Using Operations on Functions1.16.2 Composite Functions1.16.3 Components of Composite Functions1.16.4 Finding Functions That Form a Given Composite1.16.5 Finding the Difference Quotient of a Function1.17 Rational Functions1.17.1 Understanding Rational Functions1.17.2 Basic Rational Functions1.18 Graphing Rational Functions1.18.1 Vertical Asymptotes1.18.2 Horizontal Asymptotes1.18.3 Graphing Rational Functions1.18.4 Graphing Rational Functions: More Examples1.19 Function Inverses1.19.1 Understanding Inverse Functions1.19.2 The Horizontal Line Test1.19.3 Are Two Functions Inverses of Each Other?1.19.4 Graphing the Inverse1.20 Finding Function Inverses1.20.1 Finding the Inverse of a Function1.20.2 Finding the Inverse of a Function with Higher Powers

The Trigonometric Functions2.1 Angles and Radian Measure2.1.1 Finding the Quadrant in Which an Angle Lies2.1.2 Finding Coterminal Angles2.1.3 Finding the Complement and Supplement of an Angle2.1.4 Converting between Degrees and Radians2.1.5 Using the Arc Length Formula2.2 Right Angle Trigonometry2.2.1 An Introduction to the Trigonometric Functions2.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle2.2.3 Finding an Angle Given the Value of a Trigonometric Function2.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles2.2.5 Finding the Height of a Building2.3 The Trigonometric Functions2.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane2.3.2 Evaluating Trigonometric Functions Using the Reference Angle2.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions2.3.4 Trigonometric Functions of Important Angles2.4 Graphing Sine and Cosine Functions2.4.1 An Introduction to the Graphs of Sine and Cosine Functions2.4.2 Graphing Sine or Cosine Functions with Different Coefficients2.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine2.4.4 Solving Word Problems Involving Sine or Cosine Functions2.5 Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts2.5.1 Graphing Sine and Cosine Functions with Phase Shifts2.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift2.6 Graphing Other Trigonometric Functions2.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions2.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent2.6.3 Identifying a Trigonometric Function from its Graph2.7 Inverse Trigonometric Functions2.7.1 An Introduction to Inverse Trigonometric Functions2.7.2 Evaluating Inverse Trigonometric Functions2.7.3 Solving an Equation Involving an Inverse Trigonometric Function2.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse2.7.5 Applying Trigonometric Functions: Is He Speeding?

Applications of Trigonometry4.1 The Law of Sines4.1.1 The Law of Sines4.1.2 Solving a Triangle Given Two Sides and One Angle4.1.3 Solving a Triangle (SAS): Another Example4.1.4 The Law of Sines: An Application4.2 The Law of Cosines4.2.1 The Law of Cosines4.2.2 The Law of Cosines (SSS)4.2.3 The Law of Cosines (SAS): An Application4.2.4 Heron's Formula4.3 Vector Basics4.3.1 An Introduction to Vectors4.3.2 Finding the Magnitude and Direction of a Vector4.3.3 Vector Addition and Scalar Multiplication4.4 Components of Vectors and Unit Vectors4.4.1 Finding the Components of a Vector4.4.2 Finding a Unit Vector4.4.3 Solving Word Problems Involving Velocity or Forces

Complex Numbers and Polar Coordinates5.1 Complex Numbers5.1.1 Introducing and Writing Complex Numbers5.1.2 Rewriting Powers of i5.1.3 Adding and Subtracting Complex Numbers5.1.4 Multiplying Complex Numbers5.1.5 Dividing Complex Numbers5.2 Complex Numbers in Trigonometric Form5.2.1 Graphing a Complex Number and Finding Its Absolute Value5.2.2 Expressing a Complex Number in Trigonometric or Polar Form5.2.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form5.3 Powers and Roots of Complex Numbers5.3.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power5.3.2 Roots of Complex Numbers5.3.3 More Roots of Complex Numbers5.3.4 Roots of Unity5.4 Polar Coordinates5.4.1 An Introduction to Polar Coordinates5.4.2 Converting between Polar and Rectangular Coordinates5.4.3 Graphing Simple Polar Equations

Conic Sections7.1 Conic Sections: Parabolas7.1.1 An Introduction to Conic Sections7.1.2 An Introduction to Parabolas7.1.3 Determining Information about a Parabola from Its Equation7.1.4 Writing an Equation for a Parabola7.2 Conic Sections: Ellipses7.2.1 An Introduction to Ellipses7.2.2 Finding the Equation for an Ellipse7.2.3 Applying Ellipses: Satellites7.3 Conic Sections: Hyperbolas7.3.1 An Introduction to Hyperbolas7.3.2 Finding the Equation for a Hyperbola7.3.3 Applying Hyperbolas: Navigation7.4 Conic Sections7.4.1 Identifying a Conic7.4.2 Name That Conic

Edward BurgerWilliams College

Edward Burger, Professor of Mathematics at Williams College, earned hisPh.D. at the University of Texas at Austin, having graduated summa cumlaude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado atBoulder, and he served as a fellow at the University of Waterloo inCanada and at Macquarie University in Australia. Prof. Burger has wonmany awards, including the 2001 Haimo Award for Distinguished Teachingof Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. FordAward, all from the Mathematical Association of America. In 2006,Reader&apos;s Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books,including the trade book, Coincidences, Chaos, and All That Math Jazz:Making Light of Weighty Ideas and of the textbook The Heart ofMathematics: An Invitation to Effective Thinking. He also speaksfrequently to professional and public audiences, referees professionaljournals, and publishes articles in leading math journals, includingThe Journal of Number Theory and American Mathematical Monthly. Hisareas of specialty include number theory, Diophantine approximation,p-adic analysis, the geometry of numbers, and the theory of continuedfractions.

Prof. Burger's unique sense of humor and his teaching expertise combineto make him the ideal presenter of Thinkwell's entertaining andinformative video lectures.